1. Field of the Invention
The present invention relates to a quasi-TEM dielectric filter, particularly, arranged for facilitating the attainment of a small-sized structure as well as attain non-alignment and high precision.
2. Related Art Statement
In general, a band pass filter (BPF) is formed, as shown in FIG. 1, of n resonators D.sub.1, D.sub.2, . . . , D.sub.n and loads R.sub.1 and R.sub.2. In this drawing, k.sub.i, i+l indicates a coupling coefficient between resonators D.sub.i and D.sub.i+l, while Q.sub.el and Q.sub.en indicate external Q's which are obtained from resonators D.sub.l and D.sub.n coupled with loads R.sub.1 and R.sub.2 respectively. The design of the band pass filter, which is formed as mentioned above, mainly concerned with the design of coupling coefficient k.sub.i, i+l and external Q's, Q.sub.el and Q.sub.en.
In this connection, the coupling between resonators is mainly attained by the following methods.
(A) A method for coupling two resonators through a pure reactance element. PA0 (a) Coupling through a pure reactance element between resonators. PA0 (b) Coupling through an adequate structure variation provided within a symmetry plane between resonators. PA0 (c) Coupling through a dielectric wave guide from a surrounding metal face of which a conductive portion in parallel with the cross-section is removed. PA0 (B) A method for coupling two resonators through a cut-off wave guide. PA0 (C) A method for coupling two resonators through coupled distributed lines. PA0 (D) A method for coupling two resonators through uniformly coupled lines provided within a so-called nonuniform medium containing more than two dielectric mediums having individually different dielectric constants or permeabilities.
Two resonating circuits are usually coupled with each other capacitively as shown in FIGS. 2A and 2B or inductively as shown in FIGS. 2C and 2D, as follows.
For instance, central conductors of .lambda.g/4 dielectric coaxial resonators are coupled with each other through a reactance element C or L, which is an externally adopted element or an adequate electrode deposited on a ceramic material of the dielectric resonator.
For instance, as shown in FIG. 3, a hole or a groove is formed between two resonators.
In an even mode operation, no electric field exists in the vicinity of the symmetry plan as shown in FIG. 4A, so that the operation is not affected by the hole or the groove, and hence the resonant angular frequency .omega..sub.re is not greatly varied. However, in an odd mode operation, an electric field perpendicular to the symmetry plane exists as shown in FIG. 4B, so that the energy of the electric field is reduced in the vicinity of the hole or the groove, and hence the odd mode resonant angular frequency .omega..sub.ro is raised. As a result, a coupling coefficient k expressed by the following equation (1) is obtained, ##EQU1## and hence an equivalent circuit as shown in FIG. 4C is obtained.
In this connection, when a metal film is applied inside the hole or the groove as shown in FIG. 3, the even mode resonant angular frequency .omega..sub.re is not varied, while the odd mode resonant angular frequency .omega..sub.ro is lowered, because, in the odd mode operation, the path of the electric field connecting two resonators is shortened and hence capacities of these resonators are increased. As a result, an equivalent circuit is attained by coupling two resonating circuits C.sub.i L.sub.i and C.sub.j L.sub.j through a capacity C.sub.ij as shown in FIG. 5.
The coupling elements, that is L.sub.ij in FIG. 4C and C.sub.ij in FIG. 5, can be calculated according to the perturbation theory, when these coupling elements are small-sized.
The above-mentioned coupling structure can be provided on the earthed (grounded) end face of the .lambda.g/4 resonator as well as on the open end face thereof.
For instance, as shown in FIGS. 6A and 6B, a shallow hole is provide in the central portion of the earthed bottom face of the .lambda.g/4 resonator, inside which a metal film is applied. In the even mode operation, no magnetic field exists in the central portion as shown in FIG. 6C, so that the operation is not affected by the hole. However, in the odd mode operation, conductors exist in the magnetic field of the most intensity, so that the resonant angular frequency is raised according to the perturbation theory.
That is, EQU .omega..sub.re =.omega..sub.r EQU .omega..sub.ro &gt;.omega..sub.r
As a result, the equivalent circuit as shown in FIG. 4(c) is obtained.
Furthermore, various variations of shape of the coupling element can be conceived so as to obtain the difference between even mode and odd mode resonant angular frequencies. As is apparent from the above description, the variation of shape of the coupling structure in the vicinity of the symmetry plane has a large effect.
An example of this coupling structure is shown in FIG. 7A and an equivalent circuit thereof is shown in FIG. 7B. As is apparent from these drawings, the capacitive coupling can be attained in this structure.
A general arrangement therefor is shown in FIG. 8A and an example in which TE.sub.10.sup..quadrature. (i.e., TE.sub.10 rectangular mode) dielectric wave guides are coupled through a cut-off wave guide is shown in FIG. 8B, and further an equivalent circuit is shown in FIG. 8C.
Next, an example of a .lambda.g/4 multistage B.P.F. provided according to FIGS. 7A and 8B is shown in FIG. 9. In FIG. 9, the portion indicated by .delta. is operated as capacitive coupling, while the portion indicated by W is operated as inductive coupling.
On the other hand, as for a three stage B.P.F. which is formed of a combination of a .lambda.g/4 coaxial dielectric resonator and a .lambda.g/2 TE.sub.10.sup..quadrature. (i.e., TE.sub.10 rectangular mode) dielectric wave guide, the structure and the property thereof are shown in FIGS. 10A and 10B, respectively. In this multistage B.P.F., the coaxial resonator and the wave-guide resonator are inductively coupled with each other through a cutoff wave guide.
In this connection, a dielectric resonator, for instance, of TE.sub.10.sup..quadrature. mode is arranged in series with a TE cutoff wave guide, so as to be inductively coupled with each other as frequency adopted.
The TE cutoff wave guide is employed for the inductive coupling as mentioned above, while the TM cutoff wave guide can be employed for the capacitive coupling.
Coupled distributed lines consist, for instance, of two symmetrical distributed lines, earthed end portions of which cross each other. When ends on mutually opposite sides of two symmetrical distributed lines having the length (l) are earthed and the other ends thereof are opened as shown in FIG. 11A, the equivalent circuit thereof becomes as shown in FIG. 11B. In this equivalent circuit, Z.sub.e and Z.sub.o denote characteristic impedances in the case that parallel two lines as shown in FIG. 11A are excited in even mode and in odd mode, respectively. In addition, when l.perspectiveto..lambda.g/4, the equivalent circuit as shown in FIG. 11C is obtained. In this equivalent circuit, L and C are expressed by the following equation (2) ##EQU2##
Accordingly, FIG. 11C shows a circuit arrangement in which two series resonating circuits are coupled with each other through a .lambda.g/4 line having characteristic impedance of (Z.sub.e -Z.sub.o)/2. In this circuit arrangement, when even mode and odd mode exciting angular frequencies are denoted by .omega..sub.re and .omega..sub.ro respectively, the following equation (3) is obtained. ##EQU3##
As is apparent from this equation (3), EQU .omega..sub.ro &gt;.omega..sub.re ( 4)
Resonant angular frequencies .omega..sub.ro, .omega..sub.re can be obtained by substituting the equation (2) for the equation (3), while the coupling coefficient k can be obtained from the equation (1).
For the simplification, in the case that EQU Z.sub.e -Z.sub.o Z.sub.o
the relation L" L, C' C are obtained.
Accordingly, ##EQU4##
So that the coupling coefficient k is expressed by the following equation (5). ##EQU5##
It can be understood also that when the space between two conductors is increased, Z.sub.e and Z.sub.o approach the same value and k becomes smaller.
In this case, phase constants respectively regarding different modes can be varied from each other. For instance, when an air hole is formed near the midpoint between the central conductors as shown in FIGS. 12A, B, C, the effective dielectric constant is not so varied in the even mode, while it becomes smaller in the odd mode. On the other hand, the inductance per unit length is not so varied by providing the air hole in case that the cross-section of the conductor is small in comparison with the wave length, so that, the phase constant in the odd mode becomes smaller ultimately and hence the resonant frequency is raised, and, as a result, these two resonators are coupled with each other.
In general, uniformly two coupled lines within the nonuniform medium consisting of more than two kinds of mediums as shown in FIG. 13A have two different intrinsic propagation constants .beta..sub.1 and .beta..sub.2, which are expressed by the following equation (6). EQU .beta..sub.1 .noteq..beta..sub.2 . . . (6)
When, as shown in FIG. 13B, self-inductances per unit length of conductors 1 and 2 and mutual-inductance thereof are denoted by L.sub.1, L.sub.2 and M respectively, while self-capacities and mutual-capacity thereof are denoted by C.sub.11, C.sub.22 and C.sub.12 respectively, the intrinsic propagation constants .beta..sub.1, .beta..sub.2 are expressed by the following equation (7). ##EQU6##
In this equation (7), ##EQU7##
On the other hand, when the above mentioned structure has a symmetric cross-section as shown in FIG. 14, EQU L.sub.1 =L.sub.2 , C.sub.1 =C.sub.2
and hence n.sub.l =n.sub.c =1.
So that these relations are substituted for the equation (7) as follows. ##EQU8##
These constants .beta..sub.1 and .beta..sub.2 correspond to the even mode and the odd mode respectively, and hence are denoted by .beta..sub.e and .beta..sub.o respectively.
That is, EQU .beta..sub.1 =.beta..sub.e, .beta..sub.2 =.beta..sub.o ( 10)
In case that only a single medium is used, namely, in a uniform medium, the following relation can be certified. EQU k.sub.l =k.sub.c =k (11)
So that, the following condition is attained. EQU .beta..sub.e =.beta..sub.o (12)
Consequently, the relation expressed by the equation (6) can be attained only in the case of the nonuniform medium.
When both ends of two coupled lines having a length l within the nonuniform medium are short-connected, these coupled lines resonate at two angular frequencies .omega..sub.1 and .omega..sub.2, which can be obtained as follows. EQU .beta..sub.1,2 l=m.pi. 1, 2 (13)
In the equation (7) or the equation (9) of the symmetric structure, the following condition is considered, so as to obtain these frequencies.
For instance, in the case of symmetric structure, the following equation (14) is obtained. ##EQU9##
Accordingly, the relations .omega..sub.1 =.omega..sub.e and .omega..sub.2 =.omega..sub.o are substituted for the equation (1), so as to obtain the coupling coefficient k.
However, in the above-described conventional quasi-TEM mode dielectric filters, large-scaled structures formed of many constituents and difficult design and troublesome alignment caused by the complicated structures cannot be avoided as serious defects.